You multiply the quotient by the divisor to test polynomial division.
The process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition will be as follow:
- A polynomial will make up the quotient (with or without a remainder). We obtain a polynomial whose exponents and coefficients have changed by multiplying this one by the polynomial divisor. As a result, polynomials are closed when multiplied.
- The divisor normally has two or more words. By multiplying the entire quotient by each term in the divisor, we will be able to multiply the quotient by this using the distributive property. After this step is complete, we must sum the polynomials we had after multiplying them. By doing so, we have a polynomial solution whose coefficients have changed. Polynomials are hence closed under addition.
Hence we can by this way we can check polynomial division supports the fact that polynomials are closed under multiplication and addition
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